Issue 57

K. Benyahi et alii, Frattura ed Integrità Strutturale, 57 (2021) 195-222; DOI: 10.3221/IGF-ESIS.57.16

into account the limit state considered. The use of reliability methods (FORM/SORM) consists in determining the reliability index  and obtaining an approximation of the probability of failure [22].

Results of step n [K s ] n

Increased loading  P Increased internal efforts  N ,  M ,  V

Neighbor section N , M 1 = M – d.V , V Section studied N , M, V Compound bending balance N , M without interaction of force V Choose a value of the curvature  w Choose a value of the strain  u Calculate the longitudinal strain  x by the Eqn. 3 Calculate the stresses  bx and  ax by the Eqn. 18, 21 and 22, 24

Calculate the internal normal force by Eqn. 15

N int = N

Calculate the internal moment by the Eqn.16

M int = M

Calculate the distribution  (y) according to the relation which satisfies V int = V

 u ,  w known so  x (y) known,  (y) known

Equilibrium of a layer y i with  x and  known

Loop on layers Compound flexural balance with interaction of force V Calculate the stresses  ax by the Eqn. 22, Eqn. 24,  bx is known from the balance of the layers

Iteration on  u and  w to get N int = N (Eqn. 15), and M int = M (or M 1 ) (Eqn. 16) Recompute the tangential stresses with Eqn. 26 which satisfies V int = V

Check the convergence of tangential stresses

Calculate the mean distortion of the section  moy by the Eqn. 27

[ K s ] n+1 of step n+1 Calculate section stiffness  N/ Δδ u ….. Δ V/ Δγ moy

Figure 7: General flowchart of the study of a section [14].

The first step is to find the most probable point of failure * P in the space of standard variables. Then, the limit state function is approximated by its first order Taylor expansion (FORM) or second order (SORM), around the point of conception.

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